This paper combines an econometric analysis of the response of energy demand to temperature and humidity exposure with future scenarios of climate change and socioeconomic development to characterize climate impacts on energy demand at different spatial scales. Globally, future climate change is expected to have a moderate impact on energy demand, in the order of 6-11%, depending on the degree of warming, because of compensating effects across regions, fuels, and sectors. Climate-induced changes in energy demand are disproportionally larger in tropical regions. South America, Asia, and Africa, increase energy demand across all sectors and climate scenarios, while Europe, North America and Oceania exhibit mixed responses, but with consistent reductions in the residential sector. Even so, only Europe and Oceania in the moderate warming scenario experience aggregate reductions in energy use, as commercial electricity use increases significantly. We find that climate change has a regressive impact on energy demand, with the incidence of increased energy demand overwhelmingly falling on low- and middle-income countries, raising the question whether climate change could exacerbate energy poverty.